Shortness coefficient of cyclically 4-edge-connected cubic graphs
Citation Link: https://doi.org/10.15480/882.3190
Publikationstyp
Journal Article
Date Issued
2020-02-07
Sprache
English
TORE-DOI
TORE-URI
Volume
27
Issue
1
Start Page
1
End Page
12
Article Number
P1.43
Citation
Electronic Journal of Combinatorics: 1 (27): P1.43, 1-14 (2020)
Publisher DOI
Scopus ID
Grünbaum and Malkevitch proved that the shortness coefficient of cyclically 4-edge-connected cubic planar graphs is at most76 77. Recently, this was improved to (Formula Presented) and the question was raised whether this can be strengthened to 42, a natural bound inferred from one of the Faulkner-Younger graphs. We prove that the shortness coefficient of cyclically 4-edge-connected cubic planar graphs is at most 37 38 and that we also get the same value for cyclically 4-edge-connected cubic graphs of genus g for any prescribed genus g ≥ 0. We also show that45 46 is an upper bound for the shortness coefficient of cyclically 4-edge-connected cubic graphs of genus g with face lengths bounded above by some constant larger than 22 for any prescribed g ≥ 0.
DDC Class
510: Mathematik
Publication version
publishedVersion